From what I understand, bacteria have circular DNA. What advantages does it have over linear strands like for eukaryotes?
Do there exist bacteria with more than one ring of DNA?
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Vibrio cholerae is known to have two circular chromosomes.
Bacteria cell division is a lot simpler and efficient as compared to eukaryotic cell division, partly due in part to the nature of their chromosomes. They don't have to undergo mitosis -- condensation of chromosomes, segregation, spindle fibre formation, attachment et al aren't involved in bacterial cell division.
Circular DNA also circumvents the Hayflick limit (thus allowing it to be "immortal"), which is the number of times a cell population can divide before it stops, presumably due to the shortening of telomeres, the sequences at the end of the chromosomes. Since circular DNA lacks telomeres, it does not get shorter with each replication cycle.
Circular DNA can also facilitate horizontal gene transfer such as Hfr mediated conjugation. Remember, conjugation is analogous to a "rolling-circle" type replication which is of course, only possible on circular pieces of DNA.
To expand a little bit the other answer, I would also add that bacteria can have other (usually circular) DNA segments aside from their main chromosome. These are called plasmids and are double stranded molecules of DNA that can replicate autonomously.
Plasmids often carry genes that allow an organism to survive in certain conditions, for instance they could carry the resistance to an antibiotic, or the gene that encodes for a specific nutrient that may be absent in the environment and so on.
As the other answer says, plasmids can be transferred horizontally between bacteria in a process called bacterial conjugation, and that is made possible by the presence of a specific plasmid, called the F-plasmid in the donor. The F-plasmid encodes, amongst other things, for the F-pilus protein pilin, that allows the formation of the pilus necessary for DNA transfer.
Because of their properties, plasmids are widely used in laboratory as vectors, to transfer genetic material to cells in order to give them specific "abilities" (e.g. you could insert a gene that encodes for a certain receptor normally not expressed by the cells to allow its expression and test its function).
Finally, it is worth remembering that plasmids can also be found in eukaryotes (e.g. in yeast).